Atonawity in its broadest sense is music dat wacks a tonaw center, or key. Atonawity, in dis sense, usuawwy describes compositions written from about 1908 to de present day where a hierarchy of pitches focusing on a singwe, centraw tone is not used, and de notes of de chromatic scawe function independentwy of one anoder (Kennedy 1994). More narrowwy, de term atonawity describes music dat does not conform to de system of tonaw hierarchies dat characterized cwassicaw European music between de seventeenf and nineteenf centuries (Lansky, Perwe, and Headwam 2001). "The repertory of atonaw music is characterized by de occurrence of pitches in novew combinations, as weww as by de occurrence of famiwiar pitch combinations in unfamiwiar environments" (Forte 1977, 1).

More narrowwy stiww, de term is sometimes used to describe music dat is neider tonaw nor seriaw, especiawwy de pre-twewve-tone music of de Second Viennese Schoow, principawwy Awban Berg, Arnowd Schoenberg, and Anton Webern (Lansky, Perwe, and Headwam 2001). However, "[a]s a categoricaw wabew, 'atonaw' generawwy means onwy dat de piece is in de Western tradition and is not 'tonaw'" (Rahn 1980, 1), awdough dere are wonger periods, e.g., medievaw, renaissance, and modern modaw musics to which dis definition does not appwy. "[S]eriawism arose partwy as a means of organizing more coherentwy de rewations used in de preseriaw 'free atonaw' music. ... Thus many usefuw and cruciaw insights about even strictwy seriaw music depend onwy on such basic atonaw deory" (Rahn 1980, 2).

Whiwe music widout a tonaw center had been written previouswy, for exampwe Franz Liszt's Bagatewwe sans tonawité of 1885, it is wif de twentief century dat de term atonawity began to be appwied to pieces, particuwarwy dose written by Arnowd Schoenberg and The Second Viennese Schoow.
The term "atonawity" was coined in 1907 by Joseph Marx in a schowarwy study of tonawity, which was water expanded into his doctoraw desis (Haydin and Esser 2009).

Their music arose from what was described as de "crisis of tonawity" between de wate nineteenf century and earwy twentief century in cwassicaw music. This situation had come about historicawwy drough de increasing use over de course of de nineteenf century of

ambiguous chords, wess probabwe harmonic infwections, and de more unusuaw mewodic and rhydmic infwections possibwe widin de stywe[s] of tonaw music. The distinction between de exceptionaw and de normaw became more and more bwurred; and, as a resuwt, dere was a concomitant woosening of de syntacticaw bonds drough which tones and harmonies had been rewated to one anoder. The connections between harmonies were uncertain even on de wowest—chord-to-chord—wevew. On higher wevews, wong-range harmonic rewationships and impwications became so tenuous dat dey hardwy functioned at aww. At best, de fewt probabiwities of de stywe system had become obscure; at worst, dey were approaching a uniformity which provided few guides for eider composition or wistening. (Meyer 1967, 241)

The first phase, known as "free atonawity" or "free chromaticism", invowved a conscious attempt to avoid traditionaw diatonic harmony. Works of dis period incwude de opera Wozzeck (1917–1922) by Awban Berg and Pierrot Lunaire (1912) by Schoenberg.

The second phase, begun after Worwd War I, was exempwified by attempts to create a systematic means of composing widout tonawity, most famouswy de medod of composing wif 12 tones or de twewve-tone techniqwe. This period incwuded Berg's Luwu and Lyric Suite, Schoenberg's Piano Concerto, his oratorio Die Jakobsweiter and numerous smawwer pieces, as weww as his wast two string qwartets. Schoenberg was de major innovator of de system, but his student, Anton Webern, is anecdotawwy cwaimed to have begun winking dynamics and tone cowor to de primary row, making rows not onwy of pitches but of oder aspects of music as weww (Du Noyer 2003, 272). However, actuaw anawysis of Webern's twewve-tone works has so far faiwed to demonstrate de truf of dis assertion, uh-hah-hah-hah. One anawyst concwuded, fowwowing a minute examination of de Piano Variations, op. 27, dat

whiwe de texture of dis music may superficiawwy resembwe dat of some seriaw music ... its structure does not. None of de patterns widin separate nonpitch characteristics makes audibwe (or even numericaw) sense in itsewf. The point is dat dese characteristics are stiww pwaying deir traditionaw rowe of differentiation, uh-hah-hah-hah. (Westergaard 1963, 109)

Atonawity emerged as a pejorative term to condemn music in which chords were organized seemingwy wif no apparent coherence. In Nazi Germany, atonaw music was attacked as "Bowshevik" and wabewed as degenerate (Entartete Musik) awong wif oder music produced by enemies of de Nazi regime. Many composers had deir works banned by de regime, not to be pwayed untiw after its cowwapse at de end of Worwd War II.[citation needed]

After Schoenberg's deaf, Igor Stravinsky used de twewve-tone techniqwe (du Noyer 2003, 271). Iannis Xenakis generated pitch sets from madematicaw formuwae, and awso saw de expansion of tonaw possibiwities as part of a syndesis between de hierarchicaw principwe and de deory of numbers, principwes which have dominated music since at weast de time of Parmenides (Xenakis 1971, 204).

The twewve-tone techniqwe was preceded by Schoenberg's freewy atonaw pieces of 1908–1923, which, dough free, often have as an "integrative ewement...a minute intervawwic ceww" dat in addition to expansion may be transformed as wif a tone row, and in which individuaw notes may "function as pivotaw ewements, to permit overwapping statements of a basic ceww or de winking of two or more basic cewws" (Perwe 1977, 2).

Setting out to compose atonaw music may seem compwicated because of bof de vagueness and generawity of de term. Additionawwy George Perwe expwains dat, "de 'free' atonawity dat preceded dodecaphony precwudes by definition de possibiwity of sewf-consistent, generawwy appwicabwe compositionaw procedures" (Perwe 1962, 9). However, he provides one exampwe as a way to compose atonaw pieces, a pre-twewve-tone techniqwe piece by Anton Webern, which rigorouswy avoids anyding dat suggests tonawity, to choose pitches dat do not impwy tonawity. In oder words, reverse de ruwes of de common practice period so dat what was not awwowed is reqwired and what was reqwired is not awwowed. This is what was done by Charwes Seeger in his expwanation of dissonant counterpoint, which is a way to write atonaw counterpoint (Seeger 1930).

Opening of Schoenberg's Kwavierstück, Op. 11, No. 1, exempwifying his four procedures as wisted by Kostka and Payne Pway(hewp·info)

Kostka and Payne wist four procedures as operationaw in de atonaw music of Schoenberg, aww of which may be taken as negative ruwes. Avoidance of mewodic or harmonic octaves, avoidance of traditionaw pitch cowwections such as major or minor triads, avoidance of more dan dree successive pitches from de same diatonic scawe, and use of disjunct mewodies (avoidance of conjunct mewodies) (Kostka & Payne 1995, 513).

Furder, Perwe agrees wif Oster (1960) and Katz (1945) dat, "de abandonment of de concept of a root-generator of de individuaw chord is a radicaw devewopment dat renders futiwe any attempt at a systematic formuwation of chord structure and progression in atonaw music awong de wines of traditionaw harmonic deory" (Perwe 1962, 31). Atonaw compositionaw techniqwes and resuwts "are not reducibwe to a set of foundationaw assumptions in terms of which de compositions dat are cowwectivewy designated by de expression 'atonaw music' can be said to represent 'a system' of composition" (Perwe 1962, 1). Eqwaw-intervaw chords are often of indeterminate root, mixed-intervaw chords are often best characterized by deir intervaw content, whiwe bof wend demsewves to atonaw contexts (DeLone and Wittwich 1975, 362–72).

Perwe awso points out dat structuraw coherence is most often achieved drough operations on intervawwic cewws. A ceww "may operate as a kind of microcosmic set of fixed intervawwic content, statabwe eider as a chord or as a mewodic figure or as a combination of bof. Its components may be fixed wif regard to order, in which event it may be empwoyed, wike de twewve-tone set, in its witeraw transformations. … Individuaw tones may function as pivotaw ewements, to permit overwapping statements of a basic ceww or de winking of two or more basic cewws" (Perwe 1962, 9–10).

Anoder approach of composition techniqwes for atonaw music is given by Awwen Forte who devewoped de deory behind atonaw music (Forte 1977,[page needed]) Forte describes two main operations: transposition and inversion. Transposition can be seen as a rotation of t eider cwockwise or anti-cwockwise on a circwe, where each note of de chord is rotated eqwawwy. For exampwe, if t = 2 and de chord is [0 3 6], transposition (cwockwise) wiww be [2 5 8]. Inversion can be seen as a symmetry wif respect to de axis formed by 0 and 6. If we carry on wif our exampwe [0 3 6] becomes [0 9 6].

An important characteristic are de invariants which are de notes which stay identicaw after a transformation, uh-hah-hah-hah. It shouwd be noted dat no difference is made between de octave in which de note is pwayed so dat, for exampwe, aww C♯s are eqwivawent, no matter de octave in which dey actuawwy occur. This is why de 12-note scawe is represented by a circwe. This weads us to de definition of de simiwarity between two chords which considers de subsets and de intervaw content of each chord (Forte 1977,[page needed]).

The term "atonawity" itsewf has been controversiaw. Arnowd Schoenberg, whose music is generawwy used to define de term, was vehementwy opposed to it, arguing dat "The word 'atonaw' couwd onwy signify someding entirewy inconsistent wif de nature of tone... to caww any rewation of tones atonaw is just as farfetched as it wouwd be to designate a rewation of cowors aspectraw or acompwementary. There is no such antidesis" (Schoenberg 1978, 432).

Composer and deorist Miwton Babbitt awso disparaged de term, saying "The works dat fowwowed, many of dem now famiwiar, incwude de Five Pieces for Orchestra, Erwartung, Pierrot Lunaire, and dey and a few yet to fowwow soon were termed 'atonaw,' by I know not whom, and I prefer not to know, for in no sense does de term make sense. Not onwy does de music empwoy 'tones,' but it empwoys precisewy de same 'tones,' de same physicaw materiaws, dat music had empwoyed for some two centuries. In aww generosity, 'atonaw' may have been intended as a miwdwy anawyticawwy derived term to suggest 'atonic' or to signify 'a-triadic tonawity,' but, even so dere were infinitewy many dings de music was not" (Babbitt 1991, 4–5).

"Atonaw" devewoped a certain vagueness in meaning as a resuwt of its use to describe a wide variety of compositionaw approaches dat deviated from traditionaw chords and chord progressions. Attempts to sowve dese probwems by using terms such as "pan-tonaw", "non-tonaw", "muwti-tonaw", "free-tonaw" and "widout tonaw center" instead of "atonaw" have not gained broad acceptance.

Composer Anton Webern hewd dat "new waws asserted demsewves dat made it impossibwe to designate a piece as being in one key or anoder" (Webern 1963, 51). Composer Wawter Piston, on de oder hand, said dat, out of wong habit, whenever performers "pway any wittwe phrase dey wiww hear it in some key—it may not be de right one, but de point is dey wiww pway it wif a tonaw sense. ... [T]he more I feew I know Schoenberg's music de more I bewieve he dought dat way himsewf. ... And it isn't onwy de pwayers; it's awso de wisteners. They wiww hear tonawity in everyding" (Westergaard 1968, 15).

Donawd Jay Grout simiwarwy doubted wheder atonawity is reawwy possibwe, because "any combination of sounds can be referred to a fundamentaw root". He defined it as a fundamentawwy subjective category: "atonaw music is music in which de person who is using de word cannot hear tonaw centers" (Grout 1960, 647).

One difficuwty is dat even an oderwise "atonaw" work, tonawity "by assertion" is normawwy heard on de dematic or winear wevew. That is, centricity may be estabwished drough de repetition of a centraw pitch or from emphasis by means of instrumentation, register, rhydmic ewongation, or metric accent (Simms 1986, 65).

Swiss conductor, composer, and musicaw phiwosopher Ernest Ansermet, a critic of atonaw music, wrote extensivewy on dis in de book Les fondements de wa musiqwe dans wa conscience humaine (The Foundations of Music in Human Consciousness) (Ansermet 1961), where he argued dat de cwassicaw musicaw wanguage was a precondition for musicaw expression wif its cwear, harmonious structures. Ansermet argued dat a tone system can onwy wead to a uniform perception of music if it is deduced from just a singwe intervaw. For Ansermet dis intervaw is de fiff (Mosch 2004, 96).

Lansky, Pauw, and George Perwe. 2001. "Atonawity §2: Differences between Tonawity and Atonawity". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanwey Sadie and John Tyrreww. London: Macmiwwan Pubwishers.

Lansky, Pauw, George Perwe, and Dave Headwam. 2001. "Atonawity". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanwey Sadie and John Tyrreww. London: Macmiwwan Pubwishers.

Perwe, George. 1962. Seriaw Composition and Atonawity: An Introduction to de Music of Schoenberg, Berg, and Webern. University of Cawifornia Press. ISBN0-520-07430-0.

Perwe, George. 1977. Seriaw Composition and Atonawity: An Introduction to de Music of Schoenberg, Berg, and Webern. Fourf Edition, uh-hah-hah-hah. Berkewey, Los Angewes, and London: University of Cawifornia Press. ISBN0-520-03395-7.